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Table of Contents

 

 Unit 1 | Algebra

Page 1 | Expressions and Formulae

Page 2 | Index notation

Page 3| Solving Linear Equations

Page 4| Expanding and Factorising

Page 5| Factorising Quadratics and expanding double brackets

Page 6| Patterns and Sequences

Page 7| Simultaneous Equations

Page 8| Changing the subject of a Formula

Page 9| Adding , subtracting algebraic formulas

 Unit 2 |Graphs

Page 1 | Straight line graphs

Page 2 | Graphs of Quadratic functions

Unit 3 |Geometry and Measure

Page 1 | Transformations

Page 2 | Symmetry

Page 3 | Coordinates

Page 4 | Perimeter, Area, Volume

Page 5 | Circle geometry

Page 6 | Measurement

Page 7 | Trigonometry

Page 8 | Pythagoras

Page 9 | Angles

Page 10 | Shapes

Page 11| Time

Page 12 | Locus

Unit 4 | Numbers

Page 1 | Speed, Distance and time

Page 2 | Rounding and estimating

Page 3 | Ratio and proportion

Page 4 | Factors, Multiples and primes

Page 5 | Powers and roots

Page 6 | Decimals

Page 7 | Positive and negative numbers

Page 8 | Basic operations

Page 9 | Fractions

Page 10 | Percentages

Unit 5 | Statistics and Probability

Page 1 | Sampling data (MA)

Page 2 | Recording and representing data

Page 3 | Mean median range and mode

Page 4 | Standard deviation

Unit 4 | Calculus

Powers and Roots



L.O – To learn and be able to apply the rules regarding powers and roots

Powers

Powers are the mini numbers on top of ‘normal’ numbers. They are a very useful shorthand e.g. 34 is just a shorter way of writing 3x3x3x3 – the power tells us how many times to multiply 3 by itself.

1. When multiplying, add the powers

Example 1:

42 + 46 = 42+6 = 48

303 + 307 = 303+7 = 3010

Powers-and-Roots-mutiply-example1.1
2. When dividing, subtract the powers

Example 1:

65 62 = 65-2 = 63

158 – 155 = 158-5 = 153

3. When raising one power to another, multiply the powers

Example 1:

(72)4 = 72×4 = 78

(25)3 = 25×3 = 215

4. Anything to the power 1 is just itself

Example 1:

X1 = X

51 = 5

121 = 12

5. Anything to the power 0 is always 1

Example 1:

X0 = 1

30 = 1

290 = 1

6. 1 to any power is always 1

Example 1:

12 = 1

124 = 1

10 = 1

7. With fractions, apply power to top and bottom

Example 1:

Powers-and-Roots-equation-image1.1The numerator(1) and the denominator(3) of the fractions have been squared

Negative powers

If a number/fraction is raised to a negative power;

  1. Turn the number/fraction upside down
  2. Then make the power positive

Example 1:

Powers-and-Roots-native-power-example1.1 Powers-and-Roots-native-power-example1.2 Powers-and-Roots-native-power-example1.3 Powers-and-Roots-native-power-example1.4

Fractional powers

The power  means square root – √

The power  means cubed root – 3

The power  means fourth root – 4√     etc.

Example 1:

251/2 = √25 = 5

91/3 = 3√9 = 9

811/4 = 4√81 = 3

Two stage fractional powers

Some powers can be fractions like Powers-and-Roots-teo-stage-factional-power-example1.1  etc

These fractions represent a root and and a power

  1. The trick is to split the fraction into its root and power

Powers-and-Roots-teo-stage-factional-power-example1.2

  1. Once you have split the fraction, apply the root first, then the power

Example 1:

94/3

– 94/3 = (9)1/3 x 4 = (91/3)4 = 34 = 81

1253/2

– 1253/2 = (125)1/2 x 3 = (1251/2)3 = 253 = 15625

Square roots

The square root of a number can be positive or negative. There is the possibility of a negative answer as when you square a negative number, the answer is positive.

Example 1:

√ 4 = +2 or -2

√64 = +8 or -8

Questions:

Powers-and-Roots-question-image1.1Powers-and-Roots-question-image1.2Powers-and-Roots-question-image1.3Powers-and-Roots-question-image1.4Powers-and-Roots-question-image1.5Powers-and-Roots-question-image1.6Powers-and-Roots-question-image1.7Powers-and-Roots-question-image1.8Powers-and-Roots-question-image1.9Powers-and-Roots-question-image1.1.1pngPowers-and-Roots-question-image1.1.2pngPowers-and-Roots-question-image1.1.3pngPowers-and-Roots-question-image1.1.4png Powers-and-Roots-question-image1.1.5png Powers-and-Roots-question-image1.1.6png Powers-and-Roots-question-image1.1.7ngPowers-and-Roots-question-image1.1.8ngPowers-and-Roots-question-image1.1.9ngPowers-and-Roots-question-image1.2.1pngPowers-and-Roots-question-image1.2.2pngPowers-and-Roots-question-image1.2.3png Powers-and-Roots-question-image1.2.4png Powers-and-Roots-question-image1.2.5png Powers-and-Roots-question-image1.2.6png

 

 

 

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